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 Logic & Formal Reasoning


Solving stable matching problems using answer set programming

arXiv.org Artificial Intelligence

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).


Using Linear Constraints for Logic Program Termination Analysis

arXiv.org Artificial Intelligence

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their introduction is that the evaluation of a program might not terminate and checking whether it terminates or not is undecidable. To cope with this problem, several classes of logic programs have been proposed where the use of function symbols is restricted but the program evaluation termination is guaranteed. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel classes of rule-bounded and cycle-bounded programs, which overcome different limitations of current approaches by performing a more global analysis of how terms are propagated from the body to the head of rules. Results on the correctness, the complexity, and the expressivity of the proposed approach are provided.


The Rationale behind the Concept of Goal

arXiv.org Artificial Intelligence

The paper proposes a fresh look at the concept of goal and advances that motivational attitudes like desire, goal and intention are just facets of the broader notion of (acceptable) outcome. We propose to encode the preferences of an agent as sequences of "alternative acceptable outcomes". We then study how the agent's beliefs and norms can be used to filter the mental attitudes out of the sequences of alternative acceptable outcomes. Finally, we formalise such intuitions in a novel Modal Defeasible Logic and we prove that the resulting formalisation is computationally feasible.


Ethical Artificial Intelligence

arXiv.org Artificial Intelligence

This book-length article combines several peer reviewed papers and new material to analyze the issues of ethical artificial intelligence (AI). The behavior of future AI systems can be described by mathematical equations, which are adapted to analyze possible unintended AI behaviors and ways that AI designs can avoid them. This article makes the case for utility-maximizing agents and for avoiding infinite sets in agent definitions. It shows how to avoid agent self-delusion using model-based utility functions and how to avoid agents that corrupt their reward generators (sometimes called "perverse instantiation") using utility functions that evaluate outcomes at one point in time from the perspective of humans at a different point in time. It argues that agents can avoid unintended instrumental actions (sometimes called "basic AI drives" or "instrumental goals") by accurately learning human values. This article defines a self-modeling agent framework and shows how it can avoid problems of resource limits, being predicted by other agents, and inconsistency between the agent's utility function and its definition (one version of this problem is sometimes called "motivated value selection"). This article also discusses how future AI will differ from current AI, the politics of AI, and the ultimate use of AI to help understand the nature of the universe and our place in it.


SWISH: SWI-Prolog for Sharing

arXiv.org Artificial Intelligence

Recently, we see a new type of interfaces for programmers based on web technology. For example, JSFiddle, IPython Notebook and R-studio. Web technology enables cloud-based solutions, embedding in tutorial web pages, atractive rendering of results, web-scale cooperative development, etc. This article describes SWISH, a web front-end for Prolog. A public website exposes SWI-Prolog using SWISH, which is used to run small Prolog programs for demonstration, experimentation and education. We connected SWISH to the ClioPatria semantic web toolkit, where it allows for collaborative development of programs and queries related to a dataset as well as performing maintenance tasks on the running server and we embedded SWISH in the Learn Prolog Now! online Prolog book.


Expressiveness of Two-Valued Semantics for Abstract Dialectical Frameworks

Journal of Artificial Intelligence Research

By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. We also compare ADFs' expressiveness with that of (the two-valued semantics of) abstract argumentation frameworks, normal logic programs and propositional logic. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements. We finally also analyse and compare the representational succinctness of ADFs (for two-valued model semantics), that is, their capability to represent two-valued interpretation sets in a space-efficient manner.


Merits of a Temporal Modal Logic for Narrative Discourse Generation

AAAI Conferences

Just as there exists varied uses for computational models of narrative, there exists a wide variety of languages aimed at representing stories. A number of them have historic roots in automated generation, for which these languages have to be limited in order to make the generation process computationally feasible. Other are focused on story understanding, with close ties to natural language making many reasoning processes computationally intractable. In this paper, we discuss the trade-off between expressivity and computational complexity of the reasoning process and argue that Impulse, a temporal, modal logic provides more expressivity than languages historically associated with story generation, while still affording reasoning capabilities. We show that these properties enable certain aspects of narrative discourse generation by using two examples from different genres, and claim that this generalizes to a broader class of problems.


Reasoning about Truthfulness of Agents Using Answer Set Programming

AAAI Conferences

We propose a declarative framework for representing and reasoning about truthfulness  of agents using answer set programming. We show how statements by agents can be  evaluated against a set of observations over time equipped with our knowledge about  the actions of the agents and the normal behavior of agents. We illustrate the framework  using examples and discuss possible extensions that need to be considered.


Formalizing Deceptive Reasoning in Breaking Bad: Default Reasoning in a Doxastic Logic

AAAI Conferences

The rich expressivity provided by the cognitive event calculus (CEC) knowledge representation framework allows for reasoning over deeply nested beliefs, desires, intentions, and so on. I put CEC to the test by attempting to model the complex reasoning and deceptive planning used in an episode of the popular television show Breaking Bad. CEC is used to represent the knowledge used by reasoners coming up with plans like the ones devised by the fictional characters I describe. However, it becomes clear that a form of nonmonotonic reasoning is necessary—specifically so that an agent can reason about the nonmonotonic beliefs of another agent. I show how CEC can be augmented to have this ability, and then provide examples detailing how my proposed augmentation enables much of the reasoning used by agents such as the Breaking Bad characters. I close by discussing what sort of reasoning tool would be necessary to implement such nonmonotonic reasoning.


Implementing Injunctive Social Norms Using Defeasible Reasoning

AAAI Conferences

Believability requires video game characters to consider their actions within the context of social norms. Social norms involve a broad range of behavioral defaults, obligations, and injunctions unrelated to strictly causal reasoning.  Defeasible reasoning involves rationally compelling but deductively invalid arguments, such as reasoning with rules that allow exceptions. This paper investigates having video game characters use defeasible reasoning to consider injunctive social norms when selecting and planning actions.